Fant\^omas For QCD: parton distributions in a pion with B\'ezier parametrizations

TL;DR

This paper introduces a Bézier curve-based framework for parametrizing parton distribution functions, providing a stable, interpretable alternative to neural networks, and applies it to pion PDFs to enhance understanding of nonperturbative QCD.

Contribution

The paper presents a novel Bézier curve method for PDF parametrization that is stable, interpretable, and competitive with neural network approaches, specifically applied to pion PDFs.

Findings

Bézier parametrizations achieve stable fits with few parameters.

The approach offers explicit interpretability of the PDFs.

Performance is comparable to neural network-based methods.

Abstract

We report on a new framework to parametrize parton distribution functions (PDFs) and other hadronic nonperturbative functions using polynomial functions realized by B\'ezier curves. B\'ezier parameterizations produce a stable fit with a low number of free parameters, while competing in performance with neural networks and offering explicit interpretation. We specifically apply this approach to determine PDFs in a pion, essential for understanding of nonperturbative QCD dynamics.